In a water heater, a water supplying pipe and a hot-water discharging pipe are connected with a heat exchanger heated by a burner. When a faucet is opened and water is passed into the device, a controller (an operation control unit) detects passing water and operates the burner to heat the water passing through the heat exchanger. Then, the heated water is discharged from the hot-water discharging pipe. Japanese Unexamined Patent Publication No. 2008-57845 discloses a water heater including a water flow rate control unit such as a water flow rate servo or the like at the water supplying pipe. The water flow rate control unit controls a flow rate of flowing water in the heat exchanger. In this water heater, the controller controls a temperature of discharged hot water so as to male a detected temperature of discharged hot water (a temperature of discharged hot water) to be equal to a preset temperature, by control of combustion of the burner and an operation of the water flow rate control unit. The detected temperature of discharged hot water is acquired by a temperature detection unit, such as a thermistor or the like, provided at the hot-water discharging pipe.